January 15th, 2013, 07:14 AM  #1 
Newbie Joined: Jan 2013 Posts: 3 Thanks: 0  Lagrange multiplier method
So I solved a problem, but don't really know the purpose... Could it be that these to points are the maximum points or am I missing something? 
January 15th, 2013, 10:29 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Lagrange multiplier method
We are given the objective function: subject to the constraint: The method of Lagrange multipliers then gives us: Now this implies: Substituting this into the constraint, we find: and so: Although in slightly different form, my result for the critical point agrees with yours. This is the point which maximizes the objective function, or alternately, which minimizes subject to the given constraint. 

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